The finale. Summarizing the entire series, Carl describes in just a few minutes how humans evolved from a bunch of hydrogen atoms bouncing around. It instills an awareness of how unlikely and special we are, the only known intelligence in the universe, how every part of our history has helped to culminate in the world that exists today, and we are responsible for ensuring the world that the future will bring.
The very existence of the 2014 reboot. Fans of this series have been waiting a long, long time for its return.
Managing to give the show such impressive production values, so many amazing Visual Effects of Awesome, well-done animated sequences, and getting it airtime on a channel like FOX (which wouldn't normally air a show like this on Sunday nights, which is reserved for shows like Family Guy and The Simpsons) — all for a science documentary of all things — is really quite an achievement.
Seth Macfarlane also deserves a shout out. When he wants to, he can produce some very beautiful animations.
The 40 second long animation showing the evolution of life from bacteria to humans—retained in full in the 2014 reboot note (shown at the end of the 2nd episode).
Apparently Neil deGrasse Tyson can keep back wolves with just a torch The Grey style.
The depiction of Isaac Newton and Edmund Haley putting Robert Hooke in his place after he falsely claimed Newton stole his work. As unlikely as it is that Haley actually told Hooke to "put up or shut up," you can't help but cheer him on. And then Newton burns his portrait after his death, leaving no contemporary depictions of him for posterity.
Showing the lengths Clair Patterson had to go to, first to calculate the age of the Earth, and then prove the existence of lead poisoning, which has become dramatically less of a problem after his work.
In episode 4, "A Sky Full of Ghosts", Tyson completely deflates the Young Earth theory by stating that, if the universe were only 6,500 years old, most of the stars in the galaxy, not to mention the hundreds of galaxies that exist in the observable universe could not be observable. The light from anything further away from Earth than the Crab Nebula would not have had enough time to reach the Earth at light speed and be observed.